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A neural network (NN)-based adaptive control law is proposed for the tracking control of an n-link robot manipulator with unknown dynamic nonlinearities. Basis-function-like networks are employed to approximate the plant nonlinearities, and the bound on the NN reconstruction error is assumed to be unknown. The proposed NN-based adaptive control approach integrates the NN approach and an adaptive implementation of the discrete variable structure control, with a simple estimation mechanism for the upper bound on the NN reconstruction errors and an additional control input as a function of the estimate. Lyapunov stability theory is used to prove the uniform ultimate boundedness of the tracking error, and simulation results demonstrate the applicability of the proposed method to achieve desired performance.